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A traveller moves from City A to City B at 48 km/h and returns at 60 km/h. If the total time taken for the whole journey is 9 hours, find the distance between A and B.
240 km
270 km
250 km
260 km
240 km
Use the ratio of speeds (48:60=4:5). The ratio of time taken will be inverse (5:4). Total parts 5+4=9 which corresponds to 9 hours, so time taken each way is 5 hours and 4 hours respectively. Distance = 48├Ч5=240 km.
Speed from A to B is 48 km/h, speed from B to A is 60 km/h, and total time taken is 9 hours.
D=v1тАЛ+v2тАЛv1тАЛ├Чv2тАЛтАЛ├ЧTtotalтАЛ
Use the ratio of speeds (48:60=4:5). The ratio of time taken will be inverse (5:4). Total parts 5+4=9 which corresponds to 9 hours, so time taken each way is 5 hours and 4 hours respectively. Distance = 48├Ч5=240 km.
Students often calculate the average speed as 248+60тАЛ=54 and multiply by 9, which is incorrect because average speed for the round trip is the harmonic mean, not the arithmetic mean.
Define the relationship
Let the distance between A and B be d. The time taken for the first leg is 48dтАЛ and the second leg is 60dтАЛ.
48dтАЛ+60dтАЛ=9
Find the common denominator
The LCM of 48 and 60 is 240. Rewrite the equation: 2405d+4dтАЛ=9.
2409dтАЛ=9
Solve for d
Divide both sides by 9 and multiply by 240 to find the distance.
d=240
A is correct because substituting the values into the average speed formula yields a distance of 240 km.
This concept of harmonic mean is frequently tested in 'Work and Time' problems where two people finish a job at different rates and work together.
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